Circulant matrices and Galois-Togliatti systems

Pietro De Poi; Emilia Mezzetti; Mateusz Michałek; Rosa Maria Miró-Roig; Eran Nevo

doi:10.1016/j.jpaa.2020.106404

Circulant matrices and Galois-Togliatti systems

Pietro De Poi, Emilia Mezzetti, Mateusz Michałek^*, Rosa Maria Miró-Roig, Eran Nevo

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

The goal of this article is to compare the coefficients in the expansion of the permanent with those in the expansion of the determinant of a three-lines circulant matrix. As an application we solve a conjecture stated in [17] concerning the minimality of GT-systems.

Original language	American English
Article number	106404
Journal	Journal of Pure and Applied Algebra
Volume	224
Issue number	11
DOIs	https://doi.org/10.1016/j.jpaa.2020.106404
State	Published - Nov 2020

Bibliographical note

Funding Information:
Member of INdAM - GNSAGA and supported by PRIN “Geometry of algebraic varieties” 2015EYPTSB - PE1.Supported by the Polish National Science Centre grant no. 2015/19/D/ST1/01180.This work was started at the workshop “Lefschetz Properties and Jordan Type in Algebra, Geometry and Combinatorics,” held at Levico (Trento) in June 2018. The authors thank the Centro Internazionale per la Ricerca Matematica (CIRM) for its support. We also thank Nati Linial and Amir Shpilka for helpful discussions on the computational complexity aspects and for pointing us to [5].

Publisher Copyright:
© 2020 Elsevier B.V.

Keywords

Circulant matrix
Laplace equations
Monomial ideals
Permanent
Togliatti systems
Weak Lefschetz property

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10.1016/j.jpaa.2020.106404

Cite this

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abstract = "The goal of this article is to compare the coefficients in the expansion of the permanent with those in the expansion of the determinant of a three-lines circulant matrix. As an application we solve a conjecture stated in [17] concerning the minimality of GT-systems.",

keywords = "Circulant matrix, Laplace equations, Monomial ideals, Permanent, Togliatti systems, Weak Lefschetz property",

author = "{De Poi}, Pietro and Emilia Mezzetti and Mateusz Micha{\l}ek and Mir{\'o}-Roig, {Rosa Maria} and Eran Nevo",

note = "Funding Information: Member of INdAM - GNSAGA and supported by PRIN “Geometry of algebraic varieties” 2015EYPTSB - PE1.Supported by the Polish National Science Centre grant no. 2015/19/D/ST1/01180.This work was started at the workshop “Lefschetz Properties and Jordan Type in Algebra, Geometry and Combinatorics,” held at Levico (Trento) in June 2018. The authors thank the Centro Internazionale per la Ricerca Matematica (CIRM) for its support. We also thank Nati Linial and Amir Shpilka for helpful discussions on the computational complexity aspects and for pointing us to [5]. Publisher Copyright: {\textcopyright} 2020 Elsevier B.V.",

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AU - Nevo, Eran

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KW - Laplace equations

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Circulant matrices and Galois-Togliatti systems

Abstract

Bibliographical note

Keywords

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